Timing inaccessibility and the projection bound: Resolving Maxwell's demon for continuous biological substrates

Area of Science:

• Thermodynamics
• Information Theory
• Computational Biology

Background:

• Biological systems often outperform digital simulations thermodynamically.
• The Landauer limit defines the minimum energy for irreversible computation.
• Digital systems struggle with high-dimensional data and temporal complexity.

Purpose of the Study:

• To explain the thermodynamic advantage of biological continuous substrates over digital simulators.
• To quantify the energy costs associated with temporal registration and projection in biological systems.
• To establish a framework reconciling stochastic resonance and order inaccessibility.

Main Methods:

• Derivation of a Projection Bound for quasistatic projection.
• Application of a Temporal Registration Bound for order over time.
• Estimation of path degeneracy for biological processes like protein folding and neural dynamics.

Main Results:

• Biological systems exploit "timing inaccessibility" below the Landauer threshold, leading to path degeneracy.
• Projection cost scales logarithmically with degeneracy (lnG~D), contrasting with exponential digital scaling.
• Estimated biological degeneracies range from 10^42 to 10^100, depending on the process.

Conclusions:

• Continuous biological substrates achieve efficiency by integrating sub-Landauer couplings and deferring projection.
• The derived bounds quantify the gap between digital and biological computational efficiency.
• Analog and neuromorphic systems benefit from deferring projection for enhanced efficiency.